...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Memoirs of the American Mathematical Society >Volume Doubling Measures and Heat Kernel Estimates on Self-Similar Sets
【24h】

Volume Doubling Measures and Heat Kernel Estimates on Self-Similar Sets

机译：自相似集的体积加倍度量和热核估计

获取原文
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This paper studies the following three problems.1.When does a measure on a self-similar set have the volume doubling propertywith respect to a given distance?2.Is there any distance on a self-similar set under which the contraction mappingshave the prescribed values of contractions ratios?3.When does a heat kernel on a self-similar set associated with a self-similar Dirich-let form satisfy the Li-Yau type sub-Gaussian diagonal estimate?Those three problems turns out to be closely related. We introduce a new classof self-similar set, called rationally ramified self-similar sets containing both theSierpinski gasket and the (higher dimensional) Sierpinski carpet and give completesolutions of the above three problems for this class. In particular, the volume dou-bling property is shown to be equivalent to the upper Li-Yau type sub-Gaussiandiagonal estimate of a heat kernel.
机译：本文研究了以下三个问题：1，自相似集合上的度量何时具有相对于给定距离的体积倍增特性？2，自相似集合上的距离是否满足收缩映射规定3.与自相似的狄利克-莱特形式相关的自相似集上的热核何时满足李-Yau型次高斯对角线估计？这三个问题被证明是密切相关的。我们介绍了一种新的自相似集，称为合理分支自相似集，其中包含Sierpinski垫片和（高维）Sierpinski地毯，并为此类提供了以上三个问题的完整解决方案。特别地，体积倍增特性显示为与热核的上Li-Yau型亚高斯对角线估计相等。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号